6 Spatial Variations

The constraints on the variation of the fundamental constant that we have described so far are mainly
related to their cosmological evolution so that, given the Copernican principle, they reduce to constrains on
the time variation of the fundamental constants. Indeed, spatial variations can also occur. They may be
used to set constraints in two regimes:

On cosmological scales, the fields dictating the variation of the constants have fluctuations that
can let their imprint in some cosmological observables.

On local scales (e.g., our solar system or the Milky Way) the fields at the origin of the variation
of the constants are sourced by the local matter distribution so that one expect that the
constants are not homogeneous on these scales.